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A Carlson type inequality with blocks and interpolation

Natan Kruglyak, Lech Maligranda, Lars Persson (1993)

Studia Mathematica

An inequality, which generalizes and unifies some recently proved Carlson type inequalities, is proved. The inequality contains a certain number of “blocks” and it is shown that these blocks are, in a sense, optimal and cannot be removed or essentially changed. The proof is based on a special equivalent representation of a concave function (see [6, pp. 320-325]). Our Carlson type inequality is used to characterize Peetre’s interpolation functor φ (see [26]) and its Gagliardo closure on couples of...

A commutator theorem with applications.

Mario Milman (1993)

Collectanea Mathematica

We give an extension of the commutator theorems of Jawerth, Rochberg and Weiss [9] for the real method of interpolation. The results are motivated by recent work by Iwaniek and Sbordone [6] on generalized Hodge decompositions. The main estimates of these authors are based on a commutator theorem for a specific operator acting on Lp spaces and through the use of the complex method of interpolation. In this note we give an extension of the Iwaniek-Sbordone theorem to general real interpolation scales....

A note on complex interpolation of Banach lattices

Anita Tabacco Vignati, Marco Vignati (1987)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We complete a result of Hernandez on the complex interpolation for families of Banach lattices.

Absolutely (r,p,q)-summing inclusions

Carsten Michels (2007)

Studia Mathematica

As a continuation of the work of Bennett and Carl for the case q = ∞, we consider absolutely (r,p,q)-summing inclusion maps between Minkowski sequence spaces, 1 ≤ p,q ≤ 2. Using these results we deduce parts of the limit orders of the corresponding operator ideals and an inclusion theorem between the ideals of (u,s,t)-nuclear and of absolutely (r,p,q)-summing operators, which gives a new proof of a result of Carl on Schatten class operators. Furthermore, we also consider inclusions between arbitrary...

An explicit expression for the Kr functionals of interpolation between Lp spaces.

Jesús Bastero, Yves Raynaud, M. Luisa Rezola (1991)

Publicacions Matemàtiques

When dealing with interpolation spaces by real methods one is lead to compute (or at least to estimate) the K-functional associated to the couple of interpolation spaces. This concept was first introduced by J. Peetre (see [8], [9]) and some efforts have been done to find explicit expressions of it for the case of Lebesgue spaces. It is well known that for the couple consisting of L1 and L∞ on [0, ∞) K is given by K (t; f, L1, L∞) = ∫0t f* where f* denotes the non increasing rearrangement of the...

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